Find the direction, speed, and kinetic energy of a 5 kg mass moving with velocity v=⟨4,−2,6⟩v=⟨4,−2,6⟩ m/s
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Find the direction, speed, and kinetic energy of a 5 kg mass moving with velocity v=⟨4,−2,6⟩v=⟨4,−2,6⟩ m/s.

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- A person uses a set of spring-based analog scales to measure her weight. He did the weighing process 10 times and get the following measurement figures in kilograms:60.1, 59.6, 59.4, 60.4, 59.9, 59.6, 60.2, 60.7, 59.4, and 59.7. To satisfy his curiosity, he then used one scale electronically calibrated to measure its assumed weight has zero error. This scale gives a reading of 60.5 kg. Calculate the precision (precision) of a spring-based balance?The planet Earth, Jupiter, the Moon, and the Sun have the following values: mJ = 1.90x1027kg , mE = 5.97x1024kg , mM = 7.35x1022 kg , mS = 1.99x1030kg RJ = 6.99x107 m , RE = 6.37x106 m, RM = 1.74x106 m , RS = 6.96x108 m dEarth to Moon = 3.60x105 km , dEarth to Jupiter = 588x106m , dEarth to Sun = 150x106 km (a) Find the magnitude of the force of gravity acting on the planet Earth due to the planet Jupiter. (b) Find the potential energy between the planet Earth and the planet Jupiter. (c) Find the acceleration of gravity on the planet Jupiter.The error in measuring the distance of a moving object is 3.44x10^-12m. If the mass of the object is 115lb, calculate the error in measuring speed.
- If velocity =−12i + 21.5j m/s, how fast is it moving? (Express the answer to two significant figures).the average density of an atom is approximately 103 kg/m3. The nucleus of an atom has a radius about 10-5 times that of the entire atom, and contains nearly all the mass of the atom. What is the approximate density, in kilograms per cubic meter, of a nucleus?On Dec 5, 2022, scientific history was made at the Lawrence Livermore National Laboratory (LLNL) in Livermore, California when nuclear fusion was achieved when the 192 lasers deposited about 2 Megajoules (MJ) of energy into a frozen pea sized deuterium-tritium pellet and ignited the pellet through nuclear fusion to release 3 MJ of energy. The metric prefix mega means million (10^6). a) How much mass (kg) would be required to release 1 MJ of energy?
- Let A⃗ =(9,78∘) and B⃗ =(2,289∘), where the angles are measured counterclockwise from the positive x-axis. What is C⃗ =4A⃗ +B⃗ ? Give your answer in component form. x component: y component:Please use one of the following formulas: F=-k∆d f=(1/2π)(√(k/m)) T=2π√(m/k) f=(1/2π)(√(g/L)) T=2π√(L/g) v=d/t v=λf fd=fs(v+vd)/(v-vs) f=1/T T=1/f v=4Lf v=2Lf f=(1/2L)√(FT/μ)Here's how gym membership works for a potential customer: If the customer decides to join the gym, she will pay J on day 0. Then, she can use the gym starting the next day for 5 days (1; 2; 3; 4; 5), paying an additional F on each day she visits. If she goes to the gym on any given day, it costs her (10+ F) that day, but beneÖts her 30 the next day. In other words, her "costs" are a sum of her psychic costs (10) and actual Onancial costs (F). Assume that, when indi§erent, the individual will go to the gym. (a) Suppose the potential customer is a standard exponential discounter with a discount factor of = 12. If gym membership was free (i.e. J = 0 and F = 0) would she join the gym? If so, how many days would she actually go? (b) Suppose the gym did not charge a joining fee. How high could it set the usage fee? What would its revenues from this customer be? (c) Suppose instead the gym decided not to charge a usage fee. How high could it set the joining fee? [Hint: To Ögure out the…